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Math Help - Given that R is not reflexive, can R^2 be reflexive?

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    Given that R is not reflexive, can R^2 be reflexive?

    Given that R is a relation defined on a set A, and that R is not reflexive, demonstrate whether it's possible for R^2 to be reflexive.

    My first thought is that it's not possible, but I doubt that that's true...
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  2. #2
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    What about the relation "is a brother of"?
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    Quote Originally Posted by emakarov View Post
    What about the relation "is a brother of"?
    Sorry, never heard of that one. I don't think it'd work anyways.
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    Quote Originally Posted by Runty View Post
    Given that R is a relation defined on a set A, and that R is not reflexive, demonstrate whether it's possible for R^2 to be reflexive.
    By R^2 I assume that you mean R \circ R.
    If so, consider the set \{a,b\} and the relation R=\{(a,b),(b,b),(b,a)\}.
    Clearly R is not reflexive. What about R \circ R ?
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